{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trees\n",
    "\n",
    "**Definition**: An undirected tree is graph in which there is one, and only one, path between any pairs of nodes. These graphs do not have loops\n",
    "\n",
    "**Definition**: A directed tree is a graph such that there exists a single node, called the root, which has no parents, and all other nodes have one parent.\n",
    "\n",
    "### Proposition\n",
    "Any directed tree can be transformed into an undirected tree and vice versa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Directed Tree as an Undirected Tree\n",
    "Since the transformation from a directed tree to an undirected tree is achived through *moralization* (add extra links between all pairs of parent nodes) then, by definition, every node in the directed tree will have only one parent, except for the root node. Hence, we transform a directed graph to an undirected graph by simply removing the direction of the arrows."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Undirected Tree as a Directed Tree\n",
    "For every maximal clique, if any two pair of cliques share the same node, we create a directed connection from the common node to each of the remaining nodes. To see this, consider the following two examples:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### A first example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The undirected graph\n",
    "G0 = nx.Graph()\n",
    "G0.add_edges_from([(\"x1\", \"x5\"), (\"x2\", \"x5\"), (\"x3\", \"x5\"), (\"x4\", \"x5\")])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The directed graph\n",
    "G1 = nx.DiGraph()\n",
    "G1.add_edges_from([(\"x5\", \"x1\"), (\"x5\", \"x2\"), (\"x5\", \"x3\"), (\"x5\", \"x4\")])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 177,
       "width": 683
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 3))\n",
    "nx.draw(G0, labels={node:node for node in G0.nodes}, ax=ax[0])\n",
    "nx.draw(G1, labels={node:node for node in G1.nodes}, ax=ax[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### A second example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The undirected graph\n",
    "G0 = nx.Graph()\n",
    "G0.add_edges_from([(\"x1\", \"x2\"), (\"x1\", \"x3\"), (\"x2\", \"x4\"),\n",
    "                   (\"x2\", \"x5\"), (\"x3\", \"x6\"), (\"x3\", \"x7\")])\n",
    "\n",
    "G1 = nx.DiGraph()\n",
    "G1.add_edges_from([(\"x1\", \"x2\"), (\"x1\", \"x3\"), (\"x2\", \"x4\"),\n",
    "                   (\"x2\", \"x5\"), (\"x3\", \"x6\"), (\"x3\", \"x7\")])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 177,
       "width": 683
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 3))\n",
    "nx.draw(G0, labels={node:node for node in G0.nodes}, ax=ax[0])\n",
    "nx.draw(G1, labels={node:node for node in G1.nodes}, ax=ax[1])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
